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A solid sphere of mass m=2 kg and densit...

A solid sphere of mass `m=2 kg` and density `rho=500kg//m^(3)` is held stationary relative to a tank filled with water. The tank is acceerating upward with acceleration `2m//s^(2)`. Calculate
(a) Tension in the thread connected between the sphere and the bottom of the tank.
(b) If the thread snaps, calculate the acceleration of sphere with respect to the tank. (Density of water`=1000kg//m^(3),g=10m//s^(2))`

Text Solution

Verified by Experts

Density of the spherical material `=` specific gravity `xx` density of water `="sr"`
its volme is `V=m/(srho)`
Hence mass of water displaced by the shere is
`V_(rho)=m/(srho) rho=m//s=2/0.5=4kg`
since, the tank is accelerating upwards with acceleration a therefore, apparent value of gravitational acceleration is
`g'=g+a=12ms^(-2)`
Hence, upthrust exerted by water on the sphere is
`F=V_(rho)(g+a)=48N` brgt
`F=mg-T=ma=.T=F-mg-ma=24N`
When thread snaps, tension `T` disappears. Let the sphere now starts accelerating upwards with acceleration b. Considering the free body diagram.
`F-mg=mb`
`:. b=14ms^(-2)`
Thus is the absolute acceleration of the sphere. But the tank itself is accelerating upwards with acceleration a. Therefore, upward acceleration of the sphere relative to the tank is `b-a=12ms^(-2)`
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